Need help with a few questions.

Hey guys, I need help with a few questions I have to do for an assignment.

1. Radio and television stations in the USA and Canada have names that are basically four letter words. These words must begin with a K, a W, or a C and may use a blank letter as the last letter. For instance both WHO and CKLW are acceptable names.
a) How many such station names are possible?
b) How many of these are three-letter names (the last letter is a blank)?
c) How many of these names use the same letter throughout the name?

2. A bridge hand consists of 13 cards. How many bridge hands include 5 cards of one suit, 6 cards of a second, and 2 cards of a third?

Have to use combinations, permutations, or factorials for these. I don't even know where to start.

Re: Need help with a few questions.

Correct for two letters. For three letters, it is necessary to use 3-permutations when letters cannot be used more than once. There is no such restriction here. So, it's 26^2 for three letters and 26^3 for four letters.

For each starting letter (W, K and C), you need consider the total number of three- and four-letter words. Then multiply the result by 3 to get the total number of possible station names.

Re: Need help with a few questions.

Originally Posted by emakarov

Correct for two letters. For three letters, it is necessary to use 3-permutations when letters cannot be used more than once. There is no such restriction here. So, it's 26^2 for three letters and 26^3 for four letters.

For each starting letter (W, K and C), you need consider the total number of three- and four-letter words. Then multiply the result by 3 to get the total number of possible station names.

Okay so I got 3(26^2 + 26^3) = 54756 which would be the total # of possible station names.